Browsing UMBC Mathematics and Statistics Department by Issue Date
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Topics in Structured Convex Optimization and Nonlinear Programming
(20070712)A convex programming problem in a conic form is a minimization of a linear function $\langle c, x\rangle$ over the intersection of an affine space $\{x\in \mathbb{R}^n:\;Ax=b\}$ and a convex cone $K$. In this thesis, we ... 
Geomagnetic Data Assimilation Using Ensemble Methods to Estimate Forecast Error Covariance
(20071126)Data assimilation is the methodology to assimilate observational data with numerical models for better estimation of the true physical states. This research focuses on application of ensemble estimation of error covariance ... 
SpatioTemporal Modeling of Rain Rates
(20071126)Modeling episodes of heavy rain is an important component of hydrological studies. Based on the analysis of shipborne radar data over the tropical ocean, we propose a new class of probability densities that capture the ... 
PROPERTIES OF BIOEQUIVALENCE TESTS UNDER RANKED SET SAMPLING (RSS) AND SIMPLE RANDOM SAMPLING (SRS
(20071126)Bioequivalence test procedure is used in clinical trials and environmental studies. In clinical trials testing equivalence is used to assess the different formulations of two treatment drugs and the relevance of this is ... 
Convergence Order Studies for Elliptic Test Problems with COMSOL Multiphysics
(2008)The convergence order of fi nite elements is related to the polynomial order of the basis functions used on each element, with higher order polynomials yielding better convergence orders. However, two issues can prevent ... 
Parallel Performance Studies for a Hyperbolic Test Problem
(2008)The performance of parallel computer code depends on an intricate interplay of the processors, the architecture of the compute nodes, their interconnect network, the numerical algorithm, and the scheduling policy used. ... 
MVAPICH2 vs. OpenMPI for a Clustering Algorithm
(2008)Affinity propagation is a clustering algorithm that functions by identifying similar data points in an iterative process. Its structure allows for taking full advantage of parallel computing to enable the solution of larger ... 
Parallel Performance Studies for a Clustering Algorithm
(2008)Affinity propagation is a clustering algorithm that functions by identifying similar datapoints in an iterative process. Its structure allows for taking full advantage of parallel computing by enabling the solution of ... 
Parallel Performance Studies for a Parabolic Test Problem
(2008)The performance of a parallel computer depends on an intricate interplay of the processors, the architecture of the compute nodes, their interconnect network, the numerical algorithm, and the scheduling policy used. This ... 
Parallel Performance Studies for an Elliptic Test Problem
(2008)The performance of parallel computer code depends on an intricate interplay of the processors, the architecture of the compute nodes, their interconnect network, the numerical algorithm, and the scheduling policy used. The ... 
Estimation Procedures for Multinomial Models with Overdispersion
(20080101)The phenomenon of overdispersion arises when categorical or count data exhibit variability larger than expected. Multinomial data commonly demonstrate this phenomenon when the counts arise from correlated or cluster ... 
Empirical Bayes Methods for Proteomics
(20080205)Proteomics is the science that deals with highthroughput analysis of proteins. The study of proteins relies on efficient protein separation technique. 2D PAGE is a powerful technique for separating complex mixtures of ... 
Geometric optimization problems with applications to ellipsoidal approximations and quasiNewton methods
(20081009)Our goal in this dissertation is to study some optimization problems with special structure and exploit this structure to obtain additional information that will be useful in the development of numerical methods. In ... 
Partial Differential Equation Constrained Optimization and its Applications to Parameter Estimation in Models of Nerve Dendrites
(20081012)One important application of the parameter identification method in neuroscience is to determine how voltagedependent ion channels are spatially distributed through measurements of voltage along the dendrites. While in ... 
LongTime Simulations on High Resolution Meshes to Model Calcium Waves in a Heart Cell
(Society for Industrial and Applied Mathematics, 20081013)A model for the flow of calcium on the scale of one heart cell is given by a system of timedependent reactiondiffusion equations coupled by nonlinear reaction terms. Calcium ions enter into the cell at release units ... 
Efficient Computation for a ReactionDiffusion System with a Fast Reaction with Continuous and Discontinuous Initial Data Using COMSOL Multiphysics
(2009)In a chemical reactiondiffusion system with three species, the interaction between diffusion and a fast reaction between two species creates a transient, sharp, internal interface. Besides the three species model, we use ... 
Solving a TwoDimensional Elliptic Model Problem with the Conjugate Gradient Method Using MatrixFree SSOR Preconditioning in Matlab
(2009)The existing Preconditioned Conjugate Gradient method in Matlab can be optimized in terms of wall clock time and, more importantly, required storage space. The developed optimized algorithm was tested repeatedly on a two ... 
Efficient Computation for a ReactionDiffusion System with a Fast Reaction in Two Spatial Dimensions Using COMSOL Multiphysics
(2009)We study a reactiondiffusion system of three chemical species, where two chemicals react with a much faster rate than the other reaction in the model. We are interested in the asymptotic limit as the rate becomes in finite. ... 
LongTime Simulation of Calcium Waves in a Heart Cell to Study the Effects of Calcium Release Flux Density and of Coefficients in the Pump and Leak Mechanisms on SelfOrganizing Wave Behavior
(2009)Spontaneous calcium sparks can lead to propagation of a selfinitiated calcium wave under certain conditions in a heart cell. A model for diffusion waves of calcium ions in a heart cell is given by a system of coupled, ... 
Performance Studies with COMSOL Multiphysics via Scripting and Batch Processing
(2009)COMSOL Multiphysics is an extremely powerful and versatile finite element package for the solution of partial differential equations. While the graphical user interface (GUI) offers a friendly environment for solving small ...